solve the equation by completing the square. if necessary, round to the nearest hundreth.

Question

x^2-18x=19

a ) 1; 19
b ) -1; 19
c ) 3; 6
d ) -3; 1

Answer 1

To solve the equation by completing the square, first rearrange the equation to have the constant term on the right side:

x^2 - 18x = 19

Next, take half of the coefficient of x (-18) and square it:

(-18/2)^2 = 9^2 = 81

Add this value to both sides of the equation:

x^2 - 18x + 81 = 19 + 81
x^2 - 18x + 81 = 100

Now, factor the left side of the equation as a perfect square:

(x - 9)^2 = 100

Take the square root of both sides:

x - 9 = ±√100
x - 9 = ±10

Solve for x by adding 9 to both sides:

x = 9 ± 10

This gives two possible solutions:

x = 19 or x = -1

Therefore, the answer is:

b) -1; 19